Prediction of surface roughness during hard turning of AISI 4340 steel(69 HRC)

Agrawal, A., Goel, S., Rashid, W. B., & Price, M. (2015). Prediction of surface roughness during hard turning ofAISI 4340 steel (69 HRC). Applied Soft Computing, 30, 279-286. https://doi.org/10.1016/j.asoc.2015.01.059

Published in:Applied Soft Computing

Document Version:Early version, also known as pre-print

Queen's University Belfast - Research Portal:Link to publication record in Queen's University Belfast Research Portal

Publisher rightsCrown copyright © 2015 Published by Elsevier B.V. All rights reserved.This is a pre-print of an article finally published in Applied Soft Computing in May 2015: http://dx.doi.org/10.1016/j.asoc.2015.01.059

General rightsCopyright for the publications made accessible via the Queen's University Belfast Research Portal is retained by the author(s) and / or othercopyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associatedwith these rights.

Take down policyThe Research Portal is Queen's institutional repository that provides access to Queen's research output. Every effort has been made toensure that content in the Research Portal does not infringe any person's rights, or applicable UK laws. If you discover content in theResearch Portal that you believe breaches copyright or violates any law, please contact openaccess@qub.ac.uk.

Download date:14. Apr. 2020

1

Regression modelling for prediction of surface roughness during

hard turning of AISI 4340 steel (69 HRC)

Anupam Agrawala, Saurav Goel

b*, Waleed Bin Rashid

c and Mark Price

b

aDepartment of Business Administration, University of Illinois at Urbana-Champaign, USA

bSchool of Mechanical and Aerospace Engineering, Queen's University, Belfast, BT95AH, UK

cInstitute of Mechanical, Process and Energy Engineering, Heriot-Watt University, Edinburgh, UK

*Corresponding author Tel.: +44-028-90975625, Email address: s.goel@qub.ac.uk, Fax: +44-028-90974148

Abstract:

In this study, 39 sets of hard turning (HT) experimental trials were performed on a Mori-Seiki SL-

25Y (4-axis) computer numerical controlled (CNC) lathe to study the effect of cutting parameters in

influencing the machined surface roughness. In all the trials, AISI 4340 steel workpiece (hardened

up to 69 HRC) was machined with a commercially available CBN insert (Warren Tooling Limited,

UK) under dry conditions. The surface topography of the machined samples was examined by using

a white light interferometer and a reconfirmation of measurement was done using a Form Talysurf.

The machining outcome was used as an input to develop various regression models to predict the

average machined surface roughness on this material. Three regression models - Multiple

regression, Random Forest, and Quantile regression were applied to the experimental outcomes. To

the best of the authors’ knowledge, this paper is the first to apply Random Forest or Quantile

regression techniques to the machining domain. The performance of these models was compared to

each other to ascertain how feed, depth of cut, and spindle speed affect surface roughness and

finally to obtain a mathematical equation correlating these variables.

Keywords: Hard turning; Random Forest regression; Quantile regression

2

Abbreviations:

AISI American Iron and steel institute

ANOVA Analysis of variance

HT Hard turning

HRC Hardness on Rockwell ‘C’ Scale

CBN Cubic boron nitride

CNC Computer numerically controlled lathe

DOE Design of experiments

MSE Mean squared error

OOB Out of bag

GA Genetic algorithm

NN Neural Networks

RFR Random forest regression

RPM Rotation of spindle per minute

RSM Response surface methodology

var Variation

Nomenclatures:

α Constant (intercept)

εi Normally distributed error

f Feed

ap Depth of cut

t the number of trees in a Random Forest specification

m number of variables to use at each tree split in Random Forest

β Expected increment in the response

n Spindle speed (RPM)

R Tool nose radius

3

Ra Average value of machined surface roughness

Rai per unit change in surface roughness for ith

experiment

1. Introduction

Hard turning (HT) process has now become a viable method to machine automotive components

made of ferrous alloys with hardness above 45 HRC. On account of reduced lead time and

production cost, HT eliminates some of the processing steps and procedures involved during

classical machining processes for hard ferrous alloy materials; indeed, 80% of the cycle time was

saved when hard turning a pinion shaft (59-62 HRC) [1]. AISI 4340 medium carbon (0.4%C) high

strength martensitic steel is one such desirable material used very frequently to manufacture critical

components in aerospace engineering and automotive transmissions, including the manufacture of

bearings, gears, shafts, and cams, which require tighter geometric tolerances, longer service life,

and good surface finish [2]. In order to carry out a hard turning operation in a deterministic fashion,

a machine tool with high rigidity, and a cutting tool with high toughness, hardness, and chemical

inertness supplemented with appropriate machining conditions are necessary. In its current state,

hard turning differs from conventional turning on account of a number of factors including the

cutting tool, workpiece, or the process itself, all of which may influence the machining outcome.

These variables are:

1. Cutting tool: Tool rake angle, tool clearance angle, nose radius, tool material

2. Workpiece: Hardness, microstructure, grain size, workpiece material, etc.

3. Machining parameters: feed, depth of cut, cutting speed

Because of the many complexities involved, the task to machine a component with a determinisitic

level of precision becomes a challenging one. In an attempt to understand the contribution of these

variables during the hard turning of 69 HRC steel with a CBN cutting tool, 39 trials were performed

in this work.

4

2. Literature review

Hard turning owes its popularity primarily to the capability of generating complex geometric

surfaces with better form accuracy and improved tolerances in one single machining pass [3].

Previous decades of manufacturing research on hard turning have focused on finding out the

influence of tool geometry [4-5], tool wear [6-9], cutting temperature, and cutting forces [10].

Based on the outcome of these studies, the suggested cutting conditions for HT are cutting speeds

between 100 and 250 m/min, a feed rate in the range 0.05 to 0.2 mm/rev, and a depth of cut of less

than 0.25 mm [11]. A machining trial performed by Lima and co-workers [12] on AISI 4340 steel

(42 and 48 HRC) between the feed range of 0.1-0.4 mm/rev using both carbide and a PCBN insert

revealed high magnitude of cutting forces and poor machined surface. Chou et al. [13-14] found

that an increase in the tool nose radius results in an increase in the amount of specific cutting energy

and thereby an improved machined surface, but at the expense of tool wear.

Surface finish is the most common tangible outcome of any machining process that can be used to

characterize the quality of the machining since it dictates the functional properties of a machined

component. This is because surface roughness changes the contact tribology which is central to

processes ranging from adhesion to friction, wear, lubrication, and coating systems [15-16]. This, in

turn, influences the corrosion resistance, fatigue resistance, creep resistance, and service life of the

component. Therefore, manipulating machined surface roughness to high level of precision is a key

requirement of many industrial applications. In an attempt to accomplish this task, a wide variety of

soft computing tools have been applied to the domain of hard turning. Chandrasekaran et al. [17]

reviewed number of soft computing tools viz. neural networks, fuzzy sets, genetic algorithms,

simulated annealing, ant colony optimization, and particle swarm optimization, all of which can

conveniently be applied to the machining process depending on the complexity of the variable

involved. Mital et al. [18] have reviewed a great deal of literature concerning the application of

statistical methods on finish turning a variety of materials. The statistical data applied to the

experimental data in their work suggest that surface finish is primarily dependent on the type of

5

workpiece, feed rate used, and nose radius of the cutting tool.

The primary focus of this work is to investigate the influence of various machining parameters

affecting the machined surface roughness. Some of the major studies found in the literature

pertaining to the optimization of hard turning are tabulated in Table 1. It can be seen from this table

that none of the studies has attempted to optimize the hard turning of 69 HRC hardened AISI 4340

steel with a CBN tool, whereas it is very clear from the literature that workpiece hardness could be

an important variable in influencing the machined surface roughness.

In contrast to the literature detailed above, this paper focuses on modeling the results of experiments

via three regression models. Multiple regression modeling has been used in literature, however the

prevalent analysis is focused on describing the mean of the response variable for each fixed value of

the regressors, using the conditional mean of the response. This paper adds to this knowledge base

by applying the Quantile Regression technique, which fits regression curves to other parts of the

distribution of the response variable (and not merely the mean) and the Random Forest regression

(RFR) which seeks to achive higher accuracy in predicting the outcomes. The Quantile Regression

method helps to model the possibilities of different rates of change in different parts of the

probability distribution of the response variable. RFR has been shown to be superior to other soft

computing methods such as partial least squares, neural networks, and other techniques in the arena

of species distribution prediction [19], biological activity prediction [20], and genetic applications

[21], which was the motivation to apply RFR to the domain of hard turning in this work.

Table 1: Literature review of optimization studies on hard turning

Work material Tool material Optimization tools Variables studied

AISI 52100

Ceramic inserts of

aluminium oxide and

titanium carbonitride [22]

ANOVA + RSM

Cutting velocity, feed,

effective rake angle, and

nose radius

CBN cutting tool [6] ANOVA + NN

Cutting speed, feed,

workpiece hardness,

6

cutting edge geometry

Aluminium alloy 390,

Ductile case iron,

Medium carbon steel,

alloy steel, inconel

Carbide cutting tool [18] Correlation analysis

Cutting speed, feed and

nose radius (See

reference stated therein)

AISI 4140 steel

TiC coated tungsten

carbide [23-24]

Rotatable design +

Multiple regression

Cutting speed, feed,

depth of cut, time of cut

Al2O3 + TiCN mixed

ceramic [25]

ANOVA +Taguchi

Cutting speed, feed, and

depth of cut

Mild steel

TiN-coated tungsten

carbide (CNMG) [26]

RSM + GA

Speed, feed, depth of cut

and nose radius

SCM alloy 440 steel Al2O3 + TiC [27] ANOVA +Taguchi

Cutting speed, feed, and

depth of cut

SPK alloyed steel Sintered carbide [28] ANOVA + DOE

Cutting speed, feed, and

depth of cut

AISI D2 Steel Ceramic wiper inserts [29]

Multiple Regression

+ NN

Cutting speed, feed, and

cutting time

AISI 4340 steel

(below 60 HRC)

TiC/TiCN/Al2O3 coated

carbide tipped [30]

Multiple Regression

+ Taguchi + RSM

Cutting speed, feed, and

depth of cut

Zirconia toughened

alumina (ZTA) cutting

[31]

RSM + ANOVA

Cutting speed, feed, and

depth of cut

CBN, ceramic and carbide

tools [32]

Taguchi + ANOVA +

Tukey- Kramer

comparison,

Cutting speed, feed rate,

depth of cut, workpiece

hardness, and tool types

7

correlation tests

AISI H11 steel CBN tool [33] ANOVA + RSM

Cutting speed, feed rate,

depth of cut, workpiece

hardness

3. Experimental details and analysis

Longitudinal hard turning trials were performed on a Mori-Seiki SL-25Y (4-axis) CNC lathe. The

workpiece specimen used was AISI 4340 steel that was hardened up to 69 HRC through heat

treatment process. CBN cutting inserts (type CNMA 12 04 08 S-B) having a rake angle of 0°,

clearance angle of 5°, and a nose radius of 0.8 mm were procured from Warren Tooling Limited,

UK. Post-machining non-contact measurement of the surface roughness was done through a white

light interferometer (Zygo NewView 5000) and the measurements were cross checked using

Talysurf. In the subsequent section, the outcomes of the machining trials are discussed and analysed

in terms of the statistical models. Machining by mechanical means has long been a conventional

technique and unlike non-conventional machining processes it is applicable universally on almost

all the real world materials [34]. Turning is one such basic machining process in which the

workpiece is rotated at a particular speed (cutting speed) and the tool is fed against the workpiece

(feed) at a certain level of engagement (depth of cut). Essentially, the combination matrix of these

three parameters is of critical importance in determining the outcome of the process. Proper

selection of these three parameters is an essential step to make the process more accurate in terms of

the machined quality of the component and other favourable outcomes. Accordingly, the following

experimental trials were done (Table 2) which became key input to the optimisation data. Since

prior literature has shown feed (between 0.1 – 0.2 mm/rev) to be the dominant and limiting criteria

for surface roughness [2], we accordingly chose closer values to cover a range of feeds (0.08, 0.09,

0.1 and 0.15) at several depths of cut and cutting speed combinations [11].

8

3.1. Experimental data

Table 2: Experimental data obtained from the hard turning trials

Experiment # i

Feed (f)

(mm/rev)

Depth of cut (ap)

(mm)

Cutting speed (n)

(RPM)

Experimental

measurement of Ra

(micron)

1 0.08 0.1 1608 0.502

2 0.08 0.105 1250 0.532

3 0.08 0.2 858 0.5902

4 0.08 0.2 965 0.539

5 0.08 0.452 1850 0.592

6 0.08 0.542 1072 0.5693

7 0.08 0.935 1072 0.5821

8 0.09 0.083 2145 0.667

9 0.09 0.125 1000 0.735

10 0.09 0.144 1072 0.683

11 0.09 0.2 858 0.6776

12 0.09 0.2 965 0.6179

13 0.09 0.2 1072 0.742

14 0.09 0.542 965 0.718

15 0.09 0.542 1072 0.65

16 0.09 0.753 2050 0.764

17 0.09 0.935 1072 0.625

18 0.1 0.045 2145 0.77

19 0.1 0.048 2681 0.781

20 0.1 0.133 1608 0.773

21 0.1 0.2 858 0.6687

22 0.1 0.2 965 0.7029

23 0.1 0.234 2145 0.772

24 0.1 0.352 2220 0.784

25 0.1 0.542 1072 0.6769

26 0.1 0.558 1400 0.812

27 0.1 0.754 858 0.809

28 0.1 0.935 1072 0.6966

29 0.15 0.019 2681 1.251

30 0.15 0.06 1287 1.361

31 0.15 0.1 2681 1.193

32 0.15 0.2 858 1.134

33 0.15 0.2 965 1.0854

34 0.15 0.2 1072 1.316

35 0.15 0.278 1608 1.312

36 0.15 0.542 1072 1.1083

37 0.15 0.657 1600 1.345

38 0.15 0.906 2600 1.523

39 0.15 0.935 1072 1.1337

9

Table 2 present the results of the average surface roughness for various combinations of tool feed

(f), depth of cut (ap), and cutting speed (n). It can be seen from Table 2 that the best value of the

machined surface roughness obtained was 0.502 µm at a feed rate of 0.08 mm/rev, depth of cut of

0.1 mm, and cutting speed of 1608 RPM. A question may be asked as to why the feed rate was not

lowered below this point. This is because the lowering the feed rate below a certain critical rate is

governed by other factors involved in the machining operation. Below the critical feed rate,

ploughing between the cutting tool with the workpiece worsens the machined surface and hence

produces an undesirable outcome. From previous experience [35], 0.08 mm/rev was considered to

be the critical feed rate and in order to avoid any loss to the useful life of the cutting tool, this feed

was chosen as the minimum feed rate for the experiment detailed in this particular work.

3.2. Multiple regression model

First, multiple regression was applied to the data obtained from the experiment to predict the

performance parameters of hard turning as well as for the optimization of the process. In the

simplest formulation, average surface roughness (Ra) was considered to be the function of three

linear predictors: feed (f), depth of cut (ap), and RPM (n) which was modelled for the ith

experiment

by assuming a linear function as follows:

iiipii nafRa 321 (1)

Equation (1) defines a straight line. The parameter α is the constant or intercept, and represents

the error of this model estimation. The parameters β1, β2, and β3 represent the expected increment in

the response Rai per unit change in fi, api, ni respectively. The linear model in equation (1) assumes

that the three included variables are the most important determinants of surface roughness, and that

the error εi is normally distributed and uncorrelated to the variables. Model A (shown later in Table

3) shows the results of the multiple regression model specified by equation (2). Standard errors that

are robust to the assumptions outlined earlier are reported. These can be used to make valid

statistical inferences about the coefficients, even though the data are not identically distributed. The

10

regression results of Model A show that this model can explain 92.5% of variation in the data, and

the model is therefore a very reasonable predictor of surface roughness. Model A is as follows:

iipii nafRa 51061.50539.0455.9279.0 (2)

Among the three predictor variables, feed is the most significant predictor of surface roughness: the

coefficient of feed β1 is significant at a greater than 99.999 level (indicating that there is more than a

99.999% chance that feed has a strong dominance on the surface roughness). Similarly, cutting

speed is also found to be a significant predictor of surface roughness: the coefficient β3 is significant

at a >99% level. The depth of cut is not found to be a significant predictor of surface roughness.

In figure 1, the relative importance of an individual regressor’s contribution to the multiple

regression model A is analysed by using four methods. Here, relative importance refers to each

regressor’s contribution (R2) from univariate regression, and all univariate R

2 values add up to the

full model R2. The four methods used are as follows:

1. Averaging over orderings proposed by Lindeman, Merenda and Gold (LMG) [36]

2. Comparing what each regressor is able to explain in addition to all other regressors that are

available by ascribing to each regressor the increase in R2 when including this regressor as

the last of the 3 regressors in our dataset (LAST)

3. Comparing what each regressor alone is able to explain by comparing the R2 values from 3

regression models with one regressor only (FIRST)

4. Using the product of the standardized coeffcient and the marginal correlation, a measure

proposed by Hoffman and detailed by Pratt (PRATT) [37].

In this work, 1000 bootstraps were used for replications for creating 95% confidence intervals

(depicted as vertical lines within the bars in figure 1). The results show that irrespective of the

method used, feed is by far the most important predictor of surface roughness, followed by cutting

speed and depth of cut.

11

Figure 1: Relative importance of individual regressor’s contribution tested by four methods

Equation (1) presupposes that the association between dependent variable Rai and the independent

variables fi, api, and ni is additive. However, the simultaneous influence of two independent

variables (i.e. feed and depth of cut) on surface roughness may not be additive. For example, the

impact of feed may depend on the depth of cut. Such an effect is known as an interaction effect, and

these effects represent the combined effects of predictors on the dependent variable. In what

follows, equation (1) is modified to include the interaction of each pair of independent variables, as

well as the interaction of all three variables. The equation in (1) can be modified as follows:

ipiiipiiiipiiipiii anfannfafrafRa 7654321 * (3)

feed rpm dept

Method LMG

% o

f R

2

020

60

100

feed rpm dept

Method Last

% o

f R

2

020

60

100

feed rpm dept

Method First

% o

f R

2

020

60

100

feed rpm dept

Method Pratt

% o

f R

2

020

60

100

Relative Importance on Surface Roughness

with 95% bootstrap confidence intervals

R2

93.13%, metrics are normalized to sum 100%.

12

Table 3: Multiple Regression models

Dependent Variable : Surface Roughness

Base

Model

Interaction Models

A B C D E (better

model)

Feed (β1) 9.455 9.127 7.786 9.345 9.886

(0.59) (0.94) (1.49) (0.51) (1.95)

Depth of Cut (β2) 0.0539 -0.0452 0.0485 -0.271 0.414

(0.06) (0.21) (0.05) (0.08) (0.31)

RPM (β3) 5.61×10-5

5.56×10-5

-8.1×10-6

-9.8×10-6

-1.9×10-6

(2.6×10-5

) (2.5×10-5

) (9.6×10-5

) (2.2×10-5

) (2.2×10-5

)

Feed × Depth of Cut (β4) 0.892 -5.91

(2.21) (2.91)

Feed × RPM (β5) 0.00116 -5.0×10-5

(0.00) (0.00)

Depth of Cut × RPM (β6) 0.000223 -0.00019

(4.3×10-5

) (0.00)

Feed × Depth × RPM (β7) 0.00335

(0.00)

Constant -0.279 -0.242 -0.0849 -0.164 -0.223

(0.08) (0.08) (0.14) (0.05) (0.19)

Adjusted R2 0.925 0.924 0.928 0.947 0.95

No. of trials 39 39 39 39 39

Values in parentheses indicate robust Standard Errors of the coefficients

Equation (3) represents an extended model where the objective is to explore whether or not the

simultaneous effects of the three predictor variables (in pairs and all three together) are significant.

In Table 3, Models B, C, and D show the interaction effect one pair at a time, and model E shows

the interaction effect of all three variables. Adjusted R-squares have been reported for all models –

these adjust for the number of explanatory terms in a model (the adjusted R-square value increases

only if the new term improves the model more than would be expected by chance). Model B shows

that the coefficient of β4 is not significant. Model C shows that the coefficient of β5 is not

13

significant. Hence, models B and C are not significant improvements over model A. However,

model D shows that the coefficient of β6 is significant, and therefore it can be asserted that model D

is a better model to predict surface roughness than model A. Finally, model E shows that the

coefficient of β7 is significant at 99.99%, and therefore model E is also a better model to predict

surface roughness. Since Model E can explain a larger variation of data than model D (adjusted R2

is higher), Model E can therefore be chosen as the preferred model.

Overall, multiple regression results, along with the interaction terms, suggest that the following

model (E) is a better predictor of data than model A of equation (2).

piii

piiiipiiipiii

anf

annfafnafRa

00335.0

00188.01002.591.51093.1414.0886.9223.0 55

(4)

Equation (4) explains 95% of the variation in the data, and therefore is a very good fit with the

experimental data.

Overall, Multiple regression analysis helps in identifying two models that can be used for predicting

surface roughness. Model A in equation (2) is a simpler model, which can be used for quicker

prediction of the surface roughness, and can explain 92.5% of variation in the experimental data.

Model E in equation (4) is a more complex model, but can explain 95% of variation in the

experimental data.

3.3. Random Forest Regression Model

Random Forest [38] is an ensemble or divide-and-conquer approach that is similar to nearest

neighbour predictor and is used to improve the performance of prediction while using regression.

This decision tree methodology is based on machine learning technique [39] which asserts that it is

possible to achieve higher prediction accuracy by using ensembles of trees, where each tree in the

ensemble is grown in accordance with the realization of a random vector. Predictions are generated

by aggregating over the ensemble. Aggregation over the ensemble results in a reduction of variance,

14

and therefore the accuracy of the prediction is enhanced. Random Forests seek to reduce the

correlation between the aggregated quantities by drawing a subset of the covariates at random. In a

Random Forest, each node is split among a subset of predictors randomly chosen at that node. A

Random Forest algorithm for regression is as follows:

1. Draw t bootstrap samples from the original data.

2. For each of the bootstrap samples, grow a regression tree by random sampling m of the

predictors and choose the best split among those variables.

3. Predict new data by aggregating the average predictions of the t trees.

The Random Forest regression needs input data (the three predictors - feed, depth of cut, spindle

speed, and the response variable of surface roughness), the number of trees (t), and the number of

variables to use at each split (m). The random property arises out of two factors: (a) each of the t

trees is based on a random subset of the observations, and (b) each split within each tree is created

based on a random subset of m candidate variables.

Random Forests can be used to rank the importance of variables in a regression problem in a natural

way. Essentially, a Random Forest Model tries to predict the outcome variable (surface roughness)

from a group of potential predictor variables (feed, depth of cut, and cutting speed). If a predictor

variable is "important" in making the prediction accurate, then by giving it random values, we must

be able to obtain a larger impact on how well a prediction can be made, compared to a variable that

contributes little. The variable importance score tries to capture this phenomenon. More formally,

the importance of a given variable is increasing in mean square error for regression in the forest

when the observed values of this variable are randomly permuted in the samples not considered for

that tree (known as out of bag or OOB [38]). So, for each tree t of the forest, consider the associated

OOB sample. Let error1 denote the mean squared error of a single tree t on this OOB (t) sample.

Now, randomly permute the values of predictor x in the OOB (t) sample to get a perturbed sample

15

and compute the error of predictor x on the perturbed sample. Denote this by error2. Then, the

variable importance of predictor x can be denoted as )12(1

t

errorerrort

imp .

Random Forest Regression on the data was run for t = (500, 1000, 1500) and m = (1, 2, 3) to

ascertain the sensitivity of the prediction to the number of trees and the number of splits. The

number of trees (t) was increased until there was no increase in the variation explained by the

model. Table 4 provides the importance scores for the three regressors for nine sets of regressions.

A measure of the goodness-of-fit for Random Forest Regression Models is the pseudo-R2 value,

calculated from the OOB mean squared error (MSE) of the trees and the variation (var) of the

response variable (surface roughness) explained by the model as follows:

var

)(12 oobMSE

pseudoR . Table 4 also reports the pseudo-R2 values, and the model with t=500

and m=3 provided the best fit.

Table 4: Importance scores of the three regressors for RFR (seed =99)

t= 300 t= 500 t= 1000

m 3 2 1 3 2 1 3 2 1

Feed 2.665 2.347 1.749 2.672 2.344 1.757 2.678 2.347 1.754

Depth of

Cut 0.067 0.149 0.0361 0.066 0.138 0.346 0.064 0.139 0.351

RPM 0.116 0.298 0.488 0.118 0.302 0.468 0.116 0.311 0.463

Variation

(var) 89.12% 89.04% 77.85% 89.36% 88.99% 78.81% 89.23% 89.03% 80.14%

MSE

(oob) 0.0083 0.0084 0.0169 0.0081 0.0084 0.0162 0.0082 0.0084 0.0151

Pseudo

R2

0.991 0.991 0.978 0.991 0.991 0.979 0.991 0.991 0.981

The importance scores measure how much more helpful than random a particular predictor variable

is in successfully predicting the outcome variable (surface roughness). The best fit estimation

(t=500 and m=3) shows that feed is the best predictor of surface roughness, followed by spindle

16

speed (rpm) and depth of cut.

3.4. Quantile Regression Model

Quantile Regression [40] is a method for estimating relationship between variables for all portions

of a probability distribution. While multiple regressions provides a summary for the means of the

distributions corresponding to the set of regressors, Quantile regression helps to compute several

different regression curves corresponding to the various percentage points of the distributions and

thus provides a complete picture of the data. The τth

quantile could be thought of as splitting the

area under the probability density into two parts: one with area below the τth

quantile and the other

with area 1-τ above it [40]. For example, 10% of the population lies below the 10th quantile. Thus,

equation (1) for the τth

quantile will reduce to the following equation (5):

iiiii ndfRa 321 (5)

While the Multiple Regression Model specifies the change in the conditional mean of the dependent

variable (surface roughness) associated with a change in the regressors (feed, depth of cut, and

spindle speed), the Quantile Regression Model specifies changes in the conditional quantile. Thus,

the Quantile Regression model can be considered a natural extension of the Multiple Regression

model. This model can help in inspecting the rate of change of surface roughness by quantiles.

Thus, while equation (1) addresses the question “how does feed, depth of cut, and spindle speed

affect surface roughness?”, it does not and cannot answer a more nuanced question: “does feed,

depth of cut, and spindle speed influence surface roughness differently for samples with low surface

roughness than for samples with average surface roughness?” The latter question can be answered

by (for example) comparing the regression for the 50th

quantile with that for the 10th

quantile of

surface roughness.

Table 5 and figure 2 show the estimated effect of feed, depth of cut, and spindle speed on surface

roughness for the 10th

, 25th

, 50th

, 75th

and 90th

quantiles. The estimates shown here used

bootstrapped standard errors [41] with 1000 replications.

17

Table 5: Quantile Regression

Dependent variable : surface roughness

Quantile 10th

25th

50th

75th

90th

Feed 8.218 8.21 9.201 10.53 10.47

(0.42) (0.57) (1.10) (0.91) (1.04)

Depth of cut 0.0207 0.0281 0.052 0.0626 0.0362

(0.04) (0.04) (0.04) (0.04) (0.04)

RPM 6.39×10

-5 6.04×10

-5 4.51×10

-5 7.29×10

-7 0.0001

(1.9×10-5

) (1.73×10-5

) (3.1×10-5

) (4.12×10-5

) (6.7×10-5

)

Constant -0.213 -0.203 -0.251 -0.277 -0.34

(0.06) (0.06) (0.10) (0.11) (0.10)

Observations 39 39 39 39 39

Bootstrapped Standard errors in parentheses (1000 replications)

According to the Multiple Regression model A (shown earlier in Table 3), for each change of one

unit in feed rate, the average change in the mean of surface roughness is about 9.455 units. The

quantile regression results indicate that the effect of feed on surface roughness has a lower impact

for lower quantiles of surface roughness. For the 10th

quantile of surface roughness, for each change

of one unit in feed rate, the average change in the mean of surface roughness is about 8.218 units.

The Multiple Regression model overestimates this effect at the 10th

quantile. Similarly, for the 75th

quantile of surface roughness, for each change of one unit in feed rate, the average change in the

mean of surface roughness is about 10.53 units. The Multiple Regression model underestimates this

effect at the 75th

quantile.

Overall, quantile regression estimates suggest that the effect of feed on surface roughness is lower

at lower levels of surface roughness and higher as surface roughness increases. The effect of spindle

speed is in the opposite direction, i.e. the effect of spindle speed on surface roughness is higher at

lower levels of surface roughness and reduces as surface roughness increases. However, it again

becomes important as a variable at very high levels of surface roughness.

18

4. Comparison of Multiple Regression with Random Forest Regression

In this section, Multiple Regression and Random Forest Regression results are compared with each

other to evaluate their effectiveness in predicting the value of surface roughness (the Quantile

Regression methodology is not compared since that technique is used to understand how the effect

of predictor variables is different at different quantiles of surface roughness, and therefore one-on-

one comparison with other techniques is not possible). The values of the surface roughness obtained

from the 39 experimental trials, and the predicted values of the three models presented in the work

i.e. Model A (simplified multiple regression model), Model E (complex multiple regression model)

and Random Forest Regression Model are correspondingly plotted in Figure 2, Figure 3, and Figure

4 to highlight the differences of each model with respect to experimental values.

Figure 2: Comparison of experimental surface roughness with Multiple Regression Model A

19

Figure 3: Comparison of experimental surface roughness with Multiple Regression Model E

Figure 4: Comparison of experimental surface roughness with Random Forest Regression Model

20

From Figure 2, Figure 3, and Figure 4, it appears that while all three proposed models were good at

predicting the surface roughness, however they were more accurate only when the surface

roughness was below an average value of 1 micron. As the surface roughness tends to worsen

beyond 1 micron, Model E becomes more accurate than Model A because it takes into consideration

the pairing of the input variables. In general, the trend of the plot predicted by the Random Forest

Regression Model shows a lot more consistency in the values in contrast to Model E and Model A.

Finally, the standard deviations of the differences of the predicted values from the three models

versus the actual values from experiments are shown in Table 6.

Table 6: Standard deviation of the model with respect to experiments

Model A Model E RFR

Standard deviation of experimental values vs.

predicted values for the whole experiment 0.0740 0.0565 0.0465

Standard deviation of experimental values vs.

predicted values for Ra below 1 micron 0.0479 0.0447 0.0298

It can be seen that both for the surface roughness measurement below 1 micron and for the whole

set of experiments, the Random Forest Regression Model exhibits the least standard deviation

compared to the Multiple Regression Models (Model A and Model E). Also, Model E shows lower

standard deviation than Model A for the whole experiment, but for lower measure of the surface

roughness either Model A or Model E can reliably be used.

5. Conclusions

This study presents an approach of modelling comprehensive experimental trials (39 trials) to

predict the average value of machined surface roughness during hard turning of AISI 4340 steel (69

HRC) with a CBN cutting tool. For the first time, a novel approach, namely the Random Forest

Regression Model has been applied to the machining domain and an excellent correlation has been

found between the model and the experimental results, as the standard deviation of the predicted

values from the 39 experimental result sets was only 0.0465. Among the other trials, the best value

21

of the machined surface roughness obtained was 0.502 µm at a feed rate of 0.08 mm/rev, 0.1 mm

depth of cut, and cutting speed of 1608 RPM. Based on the comprehensive models developed and

proposed in this work, the following conclusions could be made:

1. Quite similar to other precision machining processes, the experimental outcome of 39 sets of

trials of hard turning of AISI 4340 steel (69 HRC) showed that the value of machined

surface roughness is most significantly impacted by the feed rate followed by the cutting

speed and depth of cut. Although the feed rate was found to play a dominant role compared

to the other two parameters, it cannot be lowered beyond a certain critical extent due to

ploughing phenomena.

2. Multiple Regression Models applied to the 39 experimental datasets obtained from in-house

trials revealed the following mathematical equations which could provide 92.5% and 95%

accurate predictions of machined surface roughness compared with the experimental results:

ipiii nafRa 51061.50539.0455.9279.0

piii

piiiipiiipiii

anf

annfafnafRa

00335.0

00188.01002.591.51093.1414.0886.9223.0 55

3. While Multiple Regression Models were found suited to addresses the question “how does

feed, depth of cut, and spindle speed affect surface roughness?”, further robustness check

was performed using the Quantile Regression Model proposed in this work which answers

the question “does feed, depth of cut, and spindle speed influence surface roughness

differently for samples with low surface roughness than for those samples with average

surface roughness?” It was found that the effect of feed on surface roughness is lower at

lower levels of surface roughness and higher as surface roughness increases. The effect of

spindle speed is in the opposite direction.

4. A novel modelling approach, i.e. Random Forest Regression, has been presented and applied

to the machining process for the first time and is found to be more accurate than Multiple

regression models in predicting surface roughness.

22

5. Multiple Regression Models were found more accurate for prediction only when the

expected surface roughness is below 1 micron. Beyond this value the results showed higher

deviation.

Acknowledgments:

Authors acknowledge the funding support of Ministry of Higher Education, Kingdom of Saudi

Arabia for funding the PhD of WBR and an additional funding from the International Research

Fellowship account of Queen’s University, Belfast.

References:

1. Rashid, W.B., S. Goel, and X. Luo. Enabling ultra high precision on hard steels using

surface defect machining. in P 7.16- Proceedings of the 14th EUSPEN International

Conference from 2nd-6th June, 2014. Dubrovnik, Croatia: EUSPEN.

2. Rashid, W.B., S. Goel, X. Luo, and J.M. Ritchie, The development of a surface defect

machining method for hard turning processes. Wear, 2013. 302(1–2): p. 1124-1135.

3. Kundrák, J., B. Karpuschewski, K. Gyani, and V. Bana, Accuracy of hard turning. Journal of

Materials Processing Technology, 2008. 202(1–3): p. 328-338.

4. Özel, T., T.-K. Hsu, and E. Zeren, Effects of cutting edge geometry, workpiece hardness, feed

rate and cutting speed on surface roughness and forces in finish turning of hardened AISI

H13 steel. The International Journal of Advanced Manufacturing Technology, 2005. 25(3-4):

p. 262-269.

5. Thiele, J.D., S.N. Melkote, R.A. Peascoe, and T.R. Watkins, Effect of Cutting-Edge

Geometry and Workpiece Hardness on Surface Residual Stresses in Finish Hard Turning of

AISI 52100 Steel. Journal of Manufacturing Science and Engineering, 2000. 122(4): p. 642-

649.

6. Özel, T. and Y. Karpat, Predictive modeling of surface roughness and tool wear in hard

turning using regression and neural networks. International Journal of Machine Tools and

Manufacture, 2005. 45(4–5): p. 467-479.

7. Kishawy, H. and M. Elbestawi, Tool wear and surface integrity during high-speed turning of

hardened steel with polycrystalline cubic boron nitride tools. Proceedings of the Institution

of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2001. 215(6): p. 755-

767.

8. Poulachon, G., A. Moisan, and I.S. Jawahir, Tool-wear mechanisms in hard turning with

polycrystalline cubic boron nitride tools. Wear, 2001. 250(1–12): p. 576-586.

9. Grzesik, W., Influence of tool wear on surface roughness in hard turning using differently

shaped ceramic tools. Wear, 2008. 265(3–4): p. 327-335.

10. Huang, Y. and S.Y. Liang, Modeling of Cutting Forces Under Hard Turning Conditions

Considering Tool Wear Effect. Journal of Manufacturing Science and Engineering, 2005.

127(2): p. 262-270.

11. Bartarya, G. and S.K. Choudhury, State of the art in hard turning. International Journal of

Machine Tools and Manufacture, 2012. 53(1): p. 1-14.

12. Lima, J.G., R.F. Ávila, A.M. Abrão, M. Faustino, and J.P. Davim, Hard turning: AISI 4340

high strength low alloy steel and AISI D2 cold work tool steel. Journal of Materials

Processing Technology, 2005. 169(3): p. 388-395.

13. Chou, Y.K., C.J. Evans, and M.M. Barash, Experimental investigation on CBN turning of

hardened AISI 52100 steel. Journal of Materials Processing Technology, 2002. 124(3): p.

23

274-283.

14. Chou, Y.K. and H. Song, Tool nose radius effects on finish hard turning. Journal of

Materials Processing Technology, 2004. 148(2): p. 259-268.

15. Buzio, R., C. Boragno, F. Biscarini, F.B. De Mongeot, and U. Valbusa, The contact

mechanics of fractal surfaces. Nature Materials, 2003. 2(4): p. 233-236.

16. Fineberg, J., Diamonds are forever - or are they? Nature Materials, 2011. 10.

17. Chandrasekaran, M., M. Muralidhar, C.M. Krishna, and U. Dixit, Application of soft

computing techniques in machining performance prediction and optimization: a literature

review. The International Journal of Advanced Manufacturing Technology, 2010. 46(5-8): p.

445-464.

18. Mital, A. and M. Mehta, Surface finish prediction models for fine turning. The International

Journal Of Production Research, 1988. 26(12): p. 1861-1876.

19. Prasad, A.M., L.R. Iverson, and A. Liaw, Newer classification and regression tree

techniques: bagging and random forests for ecological prediction. Ecosystems, 2006. 9(2):

p. 181-199.

20. Svetnik, V., A. Liaw, C. Tong, J.C. Culberson, R.P. Sheridan, and B.P. Feuston, Random

forest: a classification and regression tool for compound classification and QSAR modeling.

Journal of chemical information and computer sciences, 2003. 43(6): p. 1947-1958.

21. Bureau, A., J. Dupuis, B. Hayward, K. Falls, and P. Van Eerdewegh, Mapping complex traits

using Random Forests. BMC genetics, 2003. 4(Suppl 1): p. S64.

22. Singh, D. and P.V. Rao, A surface roughness prediction model for hard turning process. The

International Journal of Advanced Manufacturing Technology, 2007. 32(11-12): p. 1115-

1124.

23. Sundaram, R. and B. Lambert, Mathematical models to predict surface finish in fine turning

of steel. Part I. The International Journal Of Production Research, 1981. 19(5): p. 547-556.

24. Sundaram, R. and B. K LAMBERT, Mathematical models to predict surface finish in fine

turning of steel. Part II. The International Journal Of Production Research, 1981. 19(5): p.

557-564.

25. Aslan, E., N. Camuşcu, and B. Birgören, Design optimization of cutting parameters when

turning hardened AISI 4140 steel (63 HRC) with Al2O3+ TiCN mixed ceramic tool.

Materials & Design, 2007. 28(5): p. 1618-1622.

26. Suresh, P., P. Venkateswara Rao, and S. Deshmukh, A genetic algorithmic approach for

optimization of surface roughness prediction model. International Journal of Machine Tools

and Manufacture, 2002. 42(6): p. 675-680.

27. Thamizhmanii, S., S. Saparudin, and S. Hasan, Analyses of surface roughness by turning

process using Taguchi method. Journal of Achievements in Materials and Manufacturing

Engineering, 2007. 20(1-2): p. 503-506.

28. Mehrban, M., D. Naderi, V. Panahizadeh, and H.M. Naeini, Modelling of Tool Life in

Turning Process Using Experimental Method. International journal of material forming,

2008. 1(1): p. 559-562.

29. Özel, T., Y. Karpat, L. Figueira, and J.P. Davim, Modelling of surface finish and tool flank

wear in turning of AISI D2 steel with ceramic wiper inserts. Journal of Materials Processing

Technology, 2007. 189(1): p. 192-198.

30. Suresh, R., S. Basavarajappa, and G.L. Samuel, Some studies on hard turning of AISI 4340

steel using multilayer coated carbide tool. Measurement, 2012. 45(7): p. 1872-1884.

31. Mandal, N., B. Doloi, and B. Mondal, Force prediction model of Zirconia Toughened

Alumina (ZTA) inserts in hard turning of AISI 4340 steel using response surface

methodology. International Journal of Precision Engineering and Manufacturing, 2012.

13(9): p. 1589-1599.

32. Çydaş, U., Machinability evaluation in hard turning of AISI 4340 steel with different cutting

tools using statistical techniques. Proceedings of the Institution of Mechanical Engineers,

Part B: Journal of Engineering Manufacture, 2010. 224(7): p. 1043-1055.

24

33. Aouici, H., M.A. Yallese, K. Chaoui, T. Mabrouki, and J.-F. Rigal, Analysis of surface

roughness and cutting force components in hard turning with CBN tool: Prediction model

and cutting conditions optimization. Measurement, 2012. 45(3): p. 344-353.

34. Brinksmeier, E. and W. Preuss, Micro-machining. Philosophical Transactions of the Royal

Society A: Mathematical, Physical and Engineering Sciences, 2012. 370(1973): p. 3973-

3992.

35. Rashid, W.B., S. Goel, X. Luo, and J.M. Ritchie, An experimental investigation for the

improvement of attainable surface roughness during hard turning process. Proceedings of

the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2013.

227(2): p. 338-342.

36. Lindeman, R.H., P.F. Merenda, and R.Z. Gold, Introduction to bivariate and multivariate

analysis. 1980: Scott, Foresman Glenview, IL.

37. Pratt, J.W. and T. Pukkila. Dividing the indivisible: Using simple symmetry to partition

variance explained. in Proceedings of the second international conference in statistics.

1987: Tampere, Finland: University of Tampere.

38. Breiman, L., Random forests. Machine Learning, 2001. 45(1): p. 5-32.

39. Breiman, L., Bagging Predictors. Machine Learning, 1996. 24(2): p. 123-140.

40. Koenker, R. and G. Bassett Jr, Regression quantiles. Econometrica: journal of the

Econometric Society, 1978: p. 33-50.

41. Hao, L. and D.Q. Naiman, Quantile regression. Vol. 149. 2007: SAGE Publications,

Incorporated.